Engineering Board Exam Reviewer · Applications: Electric Circuits and Vibrations · hard

A series RLC circuit has L=1 H, R=6 , and C= 19 F, with no source. The charge is q(0)=1 C and the current is i(0)=0. Find q(1) in coulombs.

  1. 0.1 C
  2. 0.349 C
  3. 0.05 C
  4. 0.199 C

Answer

D. 0.199 C

Solution

q''+6q'+9q=0 has the repeated root r=-3, so q=(A+Bt)e-3t. q(0)=1 A=1. q'(0)=-3A+B=0 B=3. Then q(1)=(1+3)e-3=4e-3 0.199 C.

More Applications: Electric Circuits and Vibrations questions

  1. An undamped system obeys x''+4x=8 2t with x(0)=0 and x'(0)=0. Find x≤ft( π4 ).
  2. A damped system obeys x''+4x'+13x=0 with x(0)=1 and x'(0)=0. Find x(1).
  3. A 0.5-kg mass on a spring with k=8 N/m is pulled 0.1 m from equilibrium and released from rest (no damping). Find its displacement from…
  4. A 2-kg mass hangs on a spring with k=50 N/m and oscillates without damping. Find the period of oscillation.
  5. An RL circuit has L=0.5 H and R=20 . The current is 4 A when the source is removed and the coil discharges through the resistor. How many…
  6. A series RC circuit has R=1000 , C=100 F, and a 12-V source. The capacitor is initially uncharged. Find the capacitor voltage at t=0.2 s.
  7. A series RL circuit has L=2 H, R=10 , and a 20-V source. The current is zero at t=0. Find the current at t=0.2 s.

All Applications: Electric Circuits and Vibrations questions